Thank You Notes: A Children's Story about Exponential Growth

                                                                             

                                                                          PDF file:  vanZeeThankYouNotes.pdf

PDF file:  vanZee.Guide.ThankYouNotes.pdf


     Children’s lives have been directly impacted by the exponential-like emergence of cases of COVID-19. They also likely will experience exponential-like growth related to global climate change during their lifetimes. This book provides an emotionally positive example of exponential growth as a way to develop conceptual and mathematical understandings of this phenomenon. Also included is an example of the impact of limited resources. 

     Intended for use in grades 3-5, this book engages students in developing a mathematical understanding of exponential growth. It uses upper elementary students’ skills in multiplying by 2, adding multi-digit numbers, and creating bar graphs. The story integrates mathematics, literacy, social studies, science, and the visual arts as well as addressing many aspects of the US national standards in these curricular areas. 

     The protagonists are children engaged in an activity that upper elementary children can envision doing themselves, writing thank you notes. The story begins with questions about ways people are helping one another in their families, neighborhoods, and communities. A child, Jasmine, decides to write a thank you note and the next day asks a friend to write one too. Each day, each note writer asks a sibling or a friend to write one. Exponential growth occurs because the number of thank you notes written each day doubles. 

     The text invites readers to participate in the thinking as the children ponder how many thank you notes will be written later in the week, if each writer continues inviting someone to join them each day. They also ponder how many envelopes they will need by the end of the week (1+2+4+8+16+32+64 = 127). A parent agrees to order that many. 

     The children next contemplate continuing to write thank you notes for a second week, with each writer inviting someone to join them each day. How many envelopes will be needed then? (128+256+512+1024+2048+4096+8192 = 16,256!) A parent objects to ordering that many and instead offers to order 4 boxes of 100 envelopes each. How many more days can the children write notes if limited to only 400 more envelopes? This is an engaging way to think about what exponential growth means in terms of how the low initial stages can quickly become overwhelming and exceed limited resources. 

     The guide provides suggestions for teachers and parents interested in helping children understand what exponential growth is in a context separate from its implications during a pandemic or natural disaster. Also included are connections to US standards in mathematics, English language arts, social studies, science and the visual arts as well as to other contexts illustrating exponential growth. An outline summarizing each page may help teachers and parents plan how to use this book. Also provided is a verbatim text, page by page.